Mechanics of bending, flanging, and deep drawing and a computer-aided modeling system for predictions of strain, fracture, wrinkling and springback in sheet metal forming

This research establishes the failure criteria for localized necking, fracture, and wrinkling in sheet metal forming and the fundamentals of deformation mechanics in plane-strain bending (bending around a straight line), contour flanging (bending around a curve), and stretch/draw forming operations which are primarily used in forming the box-shaped and structural sheet components.; Mechanics of plane-strain bending and contour flanging was established. A number of commonly as well as the newly developed bending processes were analyzed. A computer code BEND was developed to simulate air bending, rotary bending, and die bending (curved-die, tractrix-die, wiping-die, U-die, and V-die). A computer program FLANGE was developed to simulate the shrink and stretch flanging operations.; The bending effects were introduced to the membrane finite element program SECTIONFORM for analyses of stretch/draw forming. In order to maintain the computational efficiency and numerical stability, a decoupled method was proposed for step-by-step bending corrections for membrane solutions. This method is able to consider both the local and the global bending effects, as well as unbending and sliding. Extra strain hardening and thinning due to bending are also included in the formulation. The simulations of the plane-strain stretch forming and deep drawing using a flat bottom punch were compared with measurements. Good agreements were achieved for three punch radii (3.18, 7.14, 9.53 mm).; A number of failure criteria were developed for bending, flanging, and stretch/draw forming operations. A new bendability criterion was proposed to determine the minimum bend ratio based on fracture mode. A localized necking criterion was established for stretch flangability analysis based on the modification of Hill's instability criterion and incorporating the strain hardening and the plastic anisotropy of sheet materials subjected to the prestrain. The wrinkling criteria for an elastic-isotropic and plastic-anisotropic shell with compound curvatures were developed to predict the body wrinkling in the unsupported region of sheet in deep drawing operations, and to determine the wrinkling at the flange edge in shrink flanging operation.; Experiments were conducted to verify the proposed process models of bending and flanging operations, and the wrinkling criteria. Simulation results were compared with measurements. The springback and the relation between bending angle vs. punch stroke in various bending operations were successfully predicted with a good accuracy. Strains and wrinkles in shrink flanging tests were predicted well.; The practical aspect of this research is to provide a scientific approach to analyze formability of complex sheet components formed by multiple operations (bending, flanging, stretching and deep drawing). The mechanics models and the associated computer-aided analysis system are able to provide information necessary for engineers to design sheet parts, processes, and dies, by a more efficient and optimum strategy which reduces and finally eliminates the costly try-outs.